Finite Group Databasebeta

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C4×#22576142 #46838884

order34688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22576142

Splittings

FittingC4×C22⋊C4×C271 ⋊ C2
SylowC271 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D271
commutatorC22×C271C23×C4
FrattiniC23C23×D271
FittingC4×C22⋊C4×C271C2
socle, cosocleC23×C271C24
prime radicalC22×C22⋊D271C22
hypercenterC4×C22⋊C4D271
hypocenterC271C4×#123
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17344

Conjugacy classes & character table

5456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 7030);