Finite Group Databasebeta

← Prev (#44552701) Next (#44552703) →

C2×C4⋊C4×Dic251 #44552702

order32128
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×Dic251

Splittings

SylowC251 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D251
commutatorC2×C251C22×C42
FrattiniC23C23×D251
FittingC22×C4⋊C4×C251C2
socle, prime radicalC24×C251C23
cosocleC23×C251C24
hypercenterC22×C4⋊C4D251
hypocenterC251C2×C4×C4⋊C4
LCSG ▷ C2×C251 ▷ C251
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32128

Conjugacy classes & character table

5080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 6847);