Finite Group Databasebeta

C2×#21437094 #29469609

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

Aliases

direct productC2×#21437094

Splittings

FittingC2×C8×Q8×C59 ⋊ C2
SylowC59 ⋊ C2×#3394

Subgroups

subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C8×Q8×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837598C2
hypercenterC2×C8×Q8D59
hypocenterC59C2×#3394
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1050488);