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C2×Q8×C4⋊Dic59 #28747992

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C4⋊Dic59

Splittings

SylowC59 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC22×C4×Q8×C59C2
socle, prime radicalC24×C59C24
cosocleC23×C59C25
hypercenterC22×C4×Q8D59
hypocenterC59C2×Q8×C4⋊C4
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C4×Q8

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328871);