Finite Group Databasebeta

C2×#23765029 #34440972

order20224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23765029

Splittings

FittingC22×M32×C79 ⋊ C2
SylowC79 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D79
commutatorC4×C79C23×C8
FrattiniC2×C8C23×D79
FittingC22×M32×C79C2
socleC22×C79C2×C22⋊C8
prime radicalC22×#11929624C4
cosocleC2×C8×C79C24
hypercenterC22×M32D79
hypocenterC79C2×#2117
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 322271);