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(C7⋊D7)⋊D55 #24924787

order10780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D55

Splittings

Fitting, socle, derived, HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D5
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ D72
SylowC72 ⋊ C2×D55
SylowC11 ⋊ D35⋊D7
SylowC5 ⋊ (C7⋊D7)⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,7^2,11|c^a=c^4,d^a=d^6,f^a=f^10,d^b=d^6,e^b=e^6

Conjugacy classes & character table

727 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44568683, (ΓL(1,𝔽8)⋊D7)⋊D55, #64424⋊D55, …
maximal normal subgroup of(ΓL(1,𝔽8)⋊D7)⋊D55, #64424⋊D55, #44568741, …
maximal quotient ofC3×(C7⋊D7)⋊D55, #44568878, #44568907

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 100);