Finite Group Databasebeta

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C4⋊C4×D116 #16822395

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D116

Splittings

FittingC4×C4⋊C4×C29 ⋊ C2
SylowC29 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC4×C4⋊C4×C29C2
socle, cosocleC23×C29C24
prime radicalC22×D116C22
hypercenterC4×C4⋊C4D29
hypocenterC29D4×C4⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 7413);