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C4⋊C4×D757 #37564340

order24224
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D757

Splittings

FittingC4⋊C4×C757 ⋊ C2
SylowC757 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D757
commutatorC2×C757C22×C4
FittingC4⋊C4×C757C2
socle, cosocleC22×C757C23
prime radicalC22×D757C22
hypercenterC4⋊C4D757
hypocenterC757C2×C4⋊C4
LCSG ▷ C2×C757 ▷ C757
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12112

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24224, 99);