Finite Group Databasebeta

C2×#21426147 #28742940

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21426147

Splittings

SylowC59 ⋊ C2×#2209

Subgroups

subgroupG/H
centerC23C2×D472
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×C4⋊C16C2
socle, prime radicalC23×C59C2×D8
hypercenterC2×C4⋊C16D59
hypocenterC59C2×#2209
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2378 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323819);