Finite Group Databasebeta

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C3×C72×Dic3×C13 #37524834

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C72×C13 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×Dic3×C13
unambiguous semidirect productC3⋊(C3×C4×C72×C13)

Splittings

derivedC3 ⋊ C3×C4×C72×C13
HallC32×C72×C13 ⋊ C4
HallC32×C72 ⋊ C4×C13
HallC32×C13 ⋊ C4×C72
SylowC32 ⋊ C4×C72×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72×C13D3
commutator, hypocenterC3C3×C4×C72×C13
FrattiniC2C3×D3×C72×C13
Fitting, socle, prime radicalC2×C32×C72×C13C2
cosocleC2×C3C2×C3×C72×C13
LCSG ▷ C3
UCSC1 ◁ C2×C3×C72×C13

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

11466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 779);