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D33⋊(C7⋊D7) #20266396

order6468
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

unambiguous semidirect productD33⋊(C7⋊D7)

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D3
HallC3×C72 ⋊ C2×D11
SylowC72 ⋊ D3×D11
HallC3×C11 ⋊ C2×C7⋊D7
SylowC11 ⋊ D3×C7⋊D7
SylowC3 ⋊ D11×C7⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C72×C11C22
LCSG ▷ C3×C72×C11
UCSC1

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,7^2,11|d^a=d^6,e^a=e^6,f^a=f^10,c^b=c^2,d^b=d^6,e^b=e^6

Conjugacy classes & character table

453 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD99⋊(C7⋊D7), D33⋊#64424, D33⋊#64425, …
maximal normal subgroup ofD33⋊#64424, D33⋊#64425, D33⋊(ΓL(1,𝔽8)⋊D7), …
maximal quotient ofD99⋊(C7⋊D7), C3×D33⋊(C7⋊D7), #34085024, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6468, 131);