Finite Group Databasebeta

C2×#21426372 #28744168

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

Aliases

direct productC2×#21426372

Splittings

SylowC59 ⋊ C2×#2253

Subgroups

subgroupG/H
centerC23C2×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#499C2
socle, prime radicalC23×C59C2×D8
hypercenterC2×#499D59
hypocenterC59C2×#2253
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#499

494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 325047);