Finite Group Databasebeta

C2×C4×(C2×D179)⋊C4 #37511331

order22912
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D179)⋊C4

Splittings

FittingC22×C42×C179 ⋊ C2
SylowC179 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D179
commutatorC2×C179C22×C42
FrattiniC23C23×D179
FittingC22×C42×C179C2
socleC24×C179C23
prime radicalC24×D179C22
cosocleC23×C179C24
hypercenterC22×C42D179
hypocenterC179C2×C4×C22⋊C4
LCSG ▷ C2×C179 ▷ C179
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11456

Conjugacy classes & character table

5776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22912, 6841);