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C7×C11⋊C5×C7⋊C9 #37564679

order24255
automorphism?
homologyAbelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊C5×C7⋊C9
unambiguous semidirect productC7⋊(C7×C9×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C7×C7⋊C9)
unambiguous semidirect product(C7×C11⋊C5)⋊(C7×C9)
unambiguous semidirect product(C11×C7⋊C9)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C7⋊C9)⋊C5

Splittings

derivedC7×C11 ⋊ C5×C7×C9
HallC7×C11×C7⋊C9 ⋊ C5
HallC72×C11⋊C5 ⋊ C9
HallC72×C11 ⋊ C5×C9
SylowC72 ⋊ C9×C11⋊C5
SylowC11 ⋊ C5×C7×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C5×C7×C9
FrattiniC3C7×ΓL(1,𝔽8)×C11⋊C5
Fitting, socleC3×C72×C11C3×C5
prime radicalC3×C72×C11⋊C5C3
cosocleC3×C7×C11C3×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C3×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 693

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 10);