Finite Group Databasebeta

C2×#21447772 #29833905

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447772

Splittings

FittingC2×C61×#349 ⋊ C2
SylowC61 ⋊ C2×#2191

Subgroups

subgroupG/H
centerC22#16839898
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#349C2
socleC22×C61#447
prime radicalC2×#16840562C2
hypercenterC2×#349D61
hypocenterC61C2×#2191
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

1128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323460);