Finite Group Databasebeta

C2×#21437674 #29495759

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#21437674

Splittings

FittingC2×C59×#533 ⋊ C2
SylowC59 ⋊ C2×Q8×#41

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#533C2
socleC23×C59C25
prime radicalC22×#11745685C22
hypercenterC2×#533D59
hypocenterC59C2×Q8×#41
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#533

7522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076638);