Finite Group Databasebeta

C2×#21424367 #28589629

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21424367

Splittings

SylowC59 ⋊ C2×#1865

Subgroups

subgroupG/H
centerC24C2×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#336C2
socle, prime radicalC24×C59C2×D4
cosocleC22×C4×C59C24
hypercenterC2×#336D59
hypocenterC59C2×#1865
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 170508);