Finite Group Databasebeta

C2×#21461554 #30614002

order15616
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#21461554

Splittings

FittingC2×C22⋊C8×C61 ⋊ C4
SylowC61 ⋊ C2×C8×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#6923
commutatorC2×C61C22×C4×C8
FrattiniC2×C4C23×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61C2×C42
prime radicalC24×D61C2×C4
cosocleC2×C4×D61C24
hypercenterC2×C22⋊C8#6923
hypocenterC61C2×C8×C22⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103557);