Finite Group Databasebeta

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C2×C22⋊C4×C22⋊D59 #28747860

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×C22⋊C4×C22⋊D59

Splittings

FittingC23×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC23×C22⋊C4×C59C2
socleC24×C59C24
prime radicalC24×C22⋊D59C2
cosocleC23×C59C25
hypercenterC23×C22⋊C4D59
hypocenterC59C2×D4×C22⋊C4
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C22⋊C4

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 328739);