Finite Group Databasebeta

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C4⋊C4×D124 #16848614

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D124

Splittings

FittingC4×C4⋊C4×C31 ⋊ C2
SylowC31 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C4⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC22×D124C22
hypercenterC4×C4⋊C4D31
hypocenterC31D4×C4⋊C4
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 7413);