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(C7⋊D7)⋊D41 #22548816

order8036
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D41
unambiguous semidirect productD287⋊D7

Splittings

Fitting, socle, derived, HallC72×C41 ⋊ C22
SylowC72 ⋊ C2×D41
SylowC41 ⋊ D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C41C22
LCSG ▷ C72×C41
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,7^2,41|c^a=c^6,e^a=e^40,c^b=c^6,d^b=d^6

Conjugacy classes & character table

545 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37563071, (ΓL(1,𝔽8)⋊D7)⋊D41, #64424⋊D41, …
maximal normal subgroup of(ΓL(1,𝔽8)⋊D7)⋊D41, #64424⋊D41, #37563103, …
maximal quotient ofC3×(C7⋊D7)⋊D41, D287⋊D21, #37563153

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8036, 26);