Finite Group Databasebeta

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C4⋊C4×Dic52 #15881352

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic52

Splittings

SylowC13 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC8×C13×C4⋊C4C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC8×C4⋊C4D13
hypocenterC13C4⋊C4×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 188001);