Finite Group Databasebeta

C2×#21447641 #29833166

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21447641

Splittings

FittingC2×C61×C22⋊C16 ⋊ C2
SylowC61 ⋊ C2×#2168

Subgroups

subgroupG/H
centerC22×C8C22×D61
commutatorC22×C61C23×C8
FrattiniC2×C8C23×D61
FittingC2×C61×C22⋊C16C2
socleC23×C61C22×C8
prime radicalC22×C22⋊D61C8
cosocleC2×C8×C61C24
hypercenterC2×C22⋊C16D61
hypocenterC61C2×#2168
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322721);