Finite Group Databasebeta

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C13×C3⋊(C3⋊(C7⋊Dic7)) #37524824

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

Aliases

direct productC13×C3⋊(C3⋊(C7⋊Dic7))
unambiguous semidirect productC3⋊(C13×C3⋊(C7⋊Dic7))
unambiguous semidirect productC7⋊(C13×C3⋊Dic21)

Splittings

derived, HallC32×C72 ⋊ C4×C13
HallC32×C72×C13 ⋊ C4
HallC72×C13 ⋊ C3⋊Dic3
HallC32×C13 ⋊ C7⋊Dic7
SylowC72 ⋊ C13×C3⋊Dic3
SylowC32 ⋊ C13×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(C3⋊(C7⋊D7))
commutator, hypocenterC32×C72C4×C13
FrattiniC2C13×C3⋊(C3⋊(C7⋊D7))
Fitting, socle, prime radicalC2×C32×C72×C13C2
cosocleC2×C32×C72C2×C13
LCSG ▷ C32×C72
UCSC1 ◁ C2×C13

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22932

Conjugacy classes & character table

5772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 769);