Finite Group Databasebeta

C22×C4⋊Dic379 #37565695

order24256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊Dic379

Splittings

SylowC379 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D379
commutatorC2×C379C23×C4
FrattiniC22C23×D379
FittingC23×C4×C379C2
socle, prime radicalC24×C379C22
cosocleC22×C379C24
hypercenterC23×C4D379
hypocenterC379C22×C4⋊C4
LCSG ▷ C2×C379 ▷ C379
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24256

Conjugacy classes & character table

6088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 1000);