Finite Group Databasebeta

← Prev (#29832987) Next (#29832989) →

C22×C4⋊#11758185 #29832988

order15616
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊#11758185

Splittings

SylowC61 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D61
commutatorC2×C61C23×C16
FrattiniC2×C8C23×D61
FittingC22×C4×C8×C61C2
socle, prime radicalC24×C61C2×C8
cosocleC2×C8×C61C24
hypercenterC22×C4×C8D61
hypocenterC61C22×C4⋊C16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322543);