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D77⋊D35 #24924785

order10780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD77⋊D35

Splittings

Fitting, socle, derived, HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D5
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ D72
SylowC72 ⋊ D5×D11
SylowC11 ⋊ D7×D35
SylowC5 ⋊ (C7⋊D7)⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,7^2,11|d^a=d^6,f^a=f^10,c^b=c^4,d^b=d^6,e^b=e^6

Conjugacy classes & character table

715 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44568681, #44568699, (C11⋊AGL(1,𝔽7))⋊D35, …
maximal normal subgroup of#44568699, (C11⋊AGL(1,𝔽7))⋊D35, #44568726, …
maximal quotient ofC3×D77⋊D35, D77⋊D105, #44568904, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 98);