Finite Group Databasebeta

C2×#21443714 #29570236

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21443714

Splittings

SylowC61 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC2×C61×#423C2
socleC23×C61#95
prime radicalC24×C61C4⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#423D61
hypocenterC61C2×#1301
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#423

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59791);