Finite Group Databasebeta

C2×D4⋊#11758185 #29589712

order15616
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×D4⋊#11758185

Splittings

SylowC61 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8C22⋊D61
commutatorC4×C61C22×C16
FrattiniC4×C8C22×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22⋊C8
prime radicalC22×D4×C61C8
cosocleC4×C8×C61C23
hypercenterC2×C8×D4D61
hypocenterC61C2×D4⋊C16
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C8×D4

470 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, 79267);