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H(3,ℤ/4)×Dic67 #30760994

order17152
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×Dic67

Splittings

SylowC67 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D67
commutatorC4×C67C43
FrattiniC23×C4C22×D67
FittingC2×H(3,ℤ/4)×C67C2
socleC22×C67C2×#95
prime radicalC24×C67C2×D4
cosocleC23×C4×C67C23
hypercenterC2×H(3,ℤ/4)D67
hypocenterC67C4×H(3,ℤ/4)
LCSG ▷ C4×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 74731);