Finite Group Databasebeta

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C4×#11758455 #16848242

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11758455

Splittings

SylowC31 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC22×C31C23×C4
FrattiniC23C23×D31
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31C4×C22⋊Q8
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 7041);