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(C7⋊D7)⋊D53 #23780747

order10388
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D53
unambiguous semidirect productD371⋊D7

Splittings

Fitting, socle, derived, HallC72×C53 ⋊ C22
SylowC53 ⋊ D72
SylowC72 ⋊ C2×D53

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C53C22
LCSG ▷ C72×C53
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,7^2,53|c^a=c^6,e^a=e^52,c^b=c^6,d^b=d^6

Conjugacy classes & character table

701 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44528394, (ΓL(1,𝔽8)⋊D7)⋊D53, #64424⋊D53, …
maximal normal subgroup of(ΓL(1,𝔽8)⋊D7)⋊D53, #64424⋊D53, #44528418, …
maximal quotient ofC3×(C7⋊D7)⋊D53, D371⋊D21, #44528468

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10388, 26);