Finite Group Databasebeta

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C22⋊C4×Dic502 #44553200

order32128
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic502

Splittings

SylowC251 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D251
commutatorC22×C251C23×C4
FittingC4×C22⋊C4×C251C2
socle, cosocleC23×C251C24
prime radicalC24×C251C23
hypercenterC4×C22⋊C4D251
hypocenterC251Q8×C22⋊C4
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16064

Conjugacy classes & character table

5050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 7345);