Finite Group Databasebeta

C2×C4×C4⋊Dic179 #37511335

order22912
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic179

Splittings

SylowC179 ⋊ C2×C4×C4⋊C4

Subgroups

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

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22912

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, 6845);