Finite Group Databasebeta

C2×#21434682 #29458433

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21434682

Splittings

SylowC59 ⋊ C2×#3170

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×C4×C8×C59C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC22×C4×C8D59
hypocenterC59C2×#3170
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1039312);