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D21⋊D77 #20266403

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

Aliases

unambiguous semidirect productD21⋊D77

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D3
HallC3×C72 ⋊ C2×D11
SylowC72 ⋊ D3×D11
HallC3×C11 ⋊ D72
SylowC11 ⋊ D21⋊D7
SylowC3 ⋊ D7×D77

Subgroups

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

104 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

Conjugacy classes & character table

471 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11725071⋊D11, D63⋊D77, #34084881, …
maximal normal subgroup of#34084881, #34084888, (C3⋊AGL(1,𝔽7))⋊D77, …
maximal quotient ofD63⋊D77, C3×D21⋊D77, #34085031, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6468, 138);