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C4×Q16×D59 #21432857

order7552
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q16×D59

Splittings

FittingC4×Q16×C59 ⋊ C2
SylowC59 ⋊ C2×C4×Q16

Subgroups

subgroupG/H
centerC2×C4D4×D59
commutatorC4×C59C23×C4
FrattiniC2×C4C23×D59
FittingC4×Q16×C59C2
socleC22×C59C22×D4
hypercenterC4×Q16D59
hypocenterC59C2×C4×Q16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

488 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD59×#1332, #28498440, D59×#1334, …
maximal normal subgroup ofD59×#1332, #28498440, D59×#1334, …
maximal quotient ofC8×Q16×D59, D59×#1584, D59×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 13271);