Finite Group Databasebeta

C22⋊C4×D823 #39912038

order26336
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D823

Splittings

FittingC22⋊C4×C823 ⋊ C2
SylowC823 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D823
commutatorC2×C823C22×C4
FittingC22⋊C4×C823C2
socle, cosocleC22×C823C23
prime radicalC23×D823C2
hypercenterC22⋊C4D823
hypocenterC823C2×C22⋊C4
LCSG ▷ C2×C823 ▷ C823
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6584

Conjugacy classes & character table

4130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26336, 96);