Finite Group Databasebeta

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C7×Dic1155 #44568518

order32340
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1155
unambiguous semidirect productC3⋊(C7×Dic385)
unambiguous semidirect productC7⋊(C7×Dic165)
unambiguous semidirect productC11⋊(C7×Dic105)

Splittings

derivedC3×C5×C7×C11 ⋊ C4×C7
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ Dic5
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ Dic15
HallC5×C72 ⋊ Dic33
HallC3×C5×C11 ⋊ C7×Dic7
HallC3×C72 ⋊ Dic55
HallC5×C11 ⋊ C7×Dic21
SylowC72 ⋊ Dic165
HallC3×C11 ⋊ C7×Dic35
HallC3×C5 ⋊ C7×Dic77
SylowC11 ⋊ C7×Dic105
SylowC5 ⋊ C7×Dic231
SylowC3 ⋊ C7×Dic385

Subgroups

subgroupG/H
center, hypercenterC2×C7D1155
commutator, hypocenterC3×C5×C7×C11C4×C7
FrattiniC2C7×D1155
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3×C5×C7×C11C2×C7
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C2×C7

144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

8106 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 220);