Finite Group Databasebeta

C2×#21426030 #28742443

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21426030

Splittings

SylowC59 ⋊ C2×#2188

Subgroups

subgroupG/H
centerC23C2×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC23×Q16×C59C2
socleC23×C59C2×D8
prime radicalC24×C59D8
hypercenterC23×Q16D59
hypocenterC59C2×#2188
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C23×Q16

1126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323322);