Finite Group Databasebeta

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C5×C11×C3⋊(C7⋊Dic7) #44568523

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C7

Aliases

direct productC5×C11×C3⋊(C7⋊Dic7)
unambiguous semidirect productC3⋊(C5×C11×C7⋊Dic7)
unambiguous semidirect productC7⋊(C5×C11×Dic21)

Splittings

derived, HallC3×C72 ⋊ C4×C5×C11
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ C4×C11
HallC72×C11 ⋊ C5×Dic3
HallC5×C72 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C7⋊Dic7
SylowC72 ⋊ C5×C11×Dic3
HallC3×C11 ⋊ C5×C7⋊Dic7
HallC3×C5 ⋊ C11×C7⋊Dic7
SylowC3 ⋊ C5×C11×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C3⋊(C7⋊D7)
commutator, hypocenterC3×C72C4×C5×C11
FrattiniC2C5×C11×C3⋊(C7⋊D7)
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3×C72C2×C5×C11
LCSG ▷ C3×C72
UCSC1 ◁ C2×C5×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 225);