Finite Group Databasebeta

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C5×Dic1155 #37528389

order23100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1155
unambiguous semidirect productC3⋊(C5×Dic385)
unambiguous semidirect productC7⋊(C5×Dic165)

Splittings

derivedC3×C5×C7×C11 ⋊ C4×C5
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ Dic21
HallC3×C7×C11 ⋊ C5×Dic5
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ C5×Dic15
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C5×Dic35
SylowC52 ⋊ Dic231
HallC3×C7 ⋊ C5×Dic55
SylowC11 ⋊ C5×Dic105
SylowC7 ⋊ C5×Dic165
SylowC3 ⋊ C5×Dic385

Subgroups

subgroupG/H
center, hypercenterC2×C5D1155
commutator, hypocenterC3×C5×C7×C11C4×C5
FrattiniC2C5×D1155
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C3×C5×C7×C11C2×C5
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C2×C5

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

normal subgroups only

This group has 128 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

5790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 200);