Finite Group Databasebeta

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C2×M16×Dic67 #22568616

order8576
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic67

Splittings

SylowC67 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D67
commutatorC2×C67C22×C42
FrattiniC2×C4C23×D67
FittingC22×M16×C67C2
socleC23×C67C22×C4
hypercenterC22×M16D67
hypocenterC67C2×C4×M16
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic67, #338×Dic67, #339×Dic67, …
maximal normal subgroup ofH(3,ℤ/4)×Dic67, #338×Dic67, #339×Dic67, …
maximal quotient ofC2×M16×C67⋊C8, C2×#22558490, C2×#22558496, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 12917);