Finite Group Databasebeta

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C4⋊C4×D719 #37527547

order23008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D719

Splittings

FittingC4⋊C4×C719 ⋊ C2
SylowC719 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D719
commutatorC2×C719C22×C4
FittingC4⋊C4×C719C2
socle, cosocleC22×C719C23
prime radicalC22×D719C22
hypercenterC4⋊C4D719
hypocenterC719C2×C4⋊C4
LCSG ▷ C2×C719 ▷ C719
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11504

Conjugacy classes & character table

3610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23008, 99);