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C11⋊C5×C3⋊(C7⋊Dic7) #44568470

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

Aliases

direct productC11⋊C5×C3⋊(C7⋊Dic7)
unambiguous semidirect productC3⋊(C11⋊C5×C7⋊Dic7)
unambiguous semidirect productC7⋊(C11⋊C5×Dic21)
unambiguous semidirect product(C11×C3⋊(C7⋊Dic7))⋊C5

Splittings

derived, HallC3×C72×C11 ⋊ C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC11×C3⋊(C7⋊Dic7) ⋊ C5
HallC72×C11⋊C5 ⋊ Dic3
HallC72×C11 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C4×C11⋊C5
SylowC72 ⋊ Dic3×C11⋊C5
HallC3×C11 ⋊ C5×C7⋊Dic7
SylowC11 ⋊ C5×C3⋊(C7⋊Dic7)
SylowC3 ⋊ C11⋊C5×C7⋊Dic7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×C3⋊(C7⋊D7)
commutator, hypocenterC3×C72×C11C4×C5
Fitting, socle, cosocleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
LCSG ▷ C3×C72×C11
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 172);