Finite Group Databasebeta

← Prev (#19150994) Next (#19150996) →

(C7⋊D7)⋊D29 #19150995

order5684
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C7⋊D7)⋊D29
unambiguous semidirect productD203⋊D7

Splittings

Fitting, socle, derived, HallC72×C29 ⋊ C22
SylowC72 ⋊ C2×D29
SylowC29 ⋊ D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C29C22
LCSG ▷ C72×C29
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,7^2,29|c^a=c^6,e^a=e^28,c^b=c^6,d^b=d^6

Conjugacy classes & character table

389 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#64424⋊D29, #30684931, (ΓL(1,𝔽8)⋊D7)⋊D29, …
maximal normal subgroup of#64424⋊D29, #30684931, (ΓL(1,𝔽8)⋊D7)⋊D29, …
maximal quotient ofC3×(C7⋊D7)⋊D29, D203⋊D21, #30685007, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5684, 42);