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(C7⋊D7)⋊D23 #17985206

order4508
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D23
unambiguous semidirect productD161⋊D7

Splittings

Fitting, socle, derived, HallC72×C23 ⋊ C22
SylowC72 ⋊ C2×D23
SylowC23 ⋊ D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C23C22
LCSG ▷ C72×C23
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 322

Polycyclic presentation:

2^2,7^2,23|c^a=c^6,e^a=e^22,c^b=c^6,d^b=d^6

Conjugacy classes & character table

311 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#64424⋊D23, #27214144, (ΓL(1,𝔽8)⋊D7)⋊D23, …
maximal normal subgroup of#64424⋊D23, #27214144, (ΓL(1,𝔽8)⋊D7)⋊D23, …
maximal quotient ofC3×(C7⋊D7)⋊D23, D161⋊D21, #27214203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4508, 21);