Finite Group Databasebeta

C2×C8×#11758226 #30544446

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×C8×#11758226

Splittings

FittingC2×C8×Q8×C61 ⋊ C2
SylowC61 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC22×C8C22×D61
commutatorC2×C61C24×C8
FrattiniC2×C4C24×D61
FittingC2×C8×Q8×C61C2
socleC23×C61C23×C4
prime radicalC22×#11758226C4
cosocleC2×C4×C61C25
hypercenterC2×C8×Q8D61
hypocenterC61C2×C8×#41
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1034001);