Finite Group Databasebeta

C2×#21437299 #29495287

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#21437299

Splittings

SylowC59 ⋊ C2×#3428

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
Fitting, prime radicalC23×#41×C59C2
socleC23×C59C25
cosocleC22×C59C26
hypercenterC23×#41D59
hypocenterC59C2×#3428
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×#41

11534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076166);