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(C7⋊D7)⋊D47 #22604257

order9212
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D47
unambiguous semidirect productD329⋊D7

Splittings

Fitting, socle, derived, HallC72×C47 ⋊ C22
SylowC72 ⋊ C2×D47
SylowC47 ⋊ D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C47C22
LCSG ▷ C72×C47
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,7^2,47|c^a=c^6,e^a=e^46,c^b=c^6,d^b=d^6

Conjugacy classes & character table

623 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#42120652, (ΓL(1,𝔽8)⋊D7)⋊D47, #64424⋊D47, …
maximal normal subgroup of(ΓL(1,𝔽8)⋊D7)⋊D47, #64424⋊D47, #42120668, …
maximal quotient ofC3×(C7⋊D7)⋊D47, D329⋊D21, #42120709

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9212, 21);