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C4⋊C4×#11761615 #30874235

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×#11761615

Splittings

FittingQ8×C4⋊C4×C67 ⋊ C2
SylowC67 ⋊ C4⋊C4×SD16

Subgroups

subgroupG/H
centerC23C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingQ8×C4⋊C4×C67C2
socleC23×C67C22×D4
prime radicalC22×D268C23
cosocleC22×C4×C67C24
hypercenterQ8×C4⋊C4D67
hypocenterC67C4⋊C4×SD16
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

1030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 187972);