Finite Group Databasebeta

C2×#21423345 #28564489

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21423345

Splittings

SylowC59 ⋊ C2×#1649

Subgroups

subgroupG/H
centerC23#14273696
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×D4×Q8×C59C2
socleC23×C59#120
prime radicalC22×D4×C59D4
hypercenterC2×D4×Q8D59
hypocenterC59C2×#1649
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4×Q8

1206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 145368);