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H(3,ℤ/4)×#64408 #34008254

order18688
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×#64408

Splittings

FittingH(3,ℤ/4)×C73 ⋊ C4
SylowC73 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC4C42×#64408
commutatorC4×C73C43
FrattiniC22×C4C22×#64408
FittingH(3,ℤ/4)×C73C4
socleC2×C73C4×#95
prime radicalC23×D73C2×D4
cosocleC22×C4×D73C23
hypercenterH(3,ℤ/4)#64408
hypocenterC73C4×H(3,ℤ/4)
LCSG ▷ C4×C73 ▷ C73
UCSC1 ◁ C4 ◁ H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1091838);