Finite Group Databasebeta

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C3×C5×C7×Dic77 #44568536

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×Dic77

Splittings

derivedC7×C11 ⋊ C3×C4×C5×C7
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C7×Dic7
HallC3×C72 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×C7×Dic7
SylowC72 ⋊ C3×C5×Dic11
HallC3×C11 ⋊ C5×C7×Dic7
SylowC11 ⋊ C3×C5×C7×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D77
commutator, hypocenterC7×C11C3×C4×C5×C7
FrattiniC2C3×C5×C7×D77
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C7×C11C2×C3×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5×C7

144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 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

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 238);