Finite Group Databasebeta

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C2×#21424662 #28590741

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21424662

Splittings

SylowC59 ⋊ C2×#1917

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×C4⋊C4×C59C2
socle, prime radicalC24×C59C22×C4
cosocleC22×C4×C59C24
hypercenterC2×C4×C4⋊C4D59
hypocenterC59C2×#1917
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171620);