Finite Group Databasebeta

C2×#21426221 #28743252

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

Aliases

direct productC2×#21426221

Splittings

SylowC59 ⋊ C2×#2222

Subgroups

subgroupG/H
centerC22#16837638
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#504C2
socleC22×C59#466
prime radicalC2×#41×C59D4
hypercenterC2×#504D59
hypocenterC59C2×#2222
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324131);