Finite Group Databasebeta

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C3×C11⋊C5×C7⋊Dic7 #44568464

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

Aliases

direct productC3×C11⋊C5×C7⋊Dic7
unambiguous semidirect product(C3×C11×C7⋊Dic7)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC3×C11×C7⋊Dic7 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC11×C7⋊Dic7 ⋊ C3×C5
HallC3×C72×C11 ⋊ C4×C5
HallC3×C72 ⋊ C4×C11⋊C5
SylowC72 ⋊ C3×C4×C11⋊C5
HallC3×C11 ⋊ C5×C7⋊Dic7
SylowC11 ⋊ C3×C5×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×C7⋊D7
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C3×C11⋊C5×C7⋊D7
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 166);