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C4×C22⋊D67 #14524004

order2144
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D67

Splittings

FittingC22×C4×C67 ⋊ C2
SylowC67 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D67
commutatorC2×C67C22×C4
FrattiniC22C22×D67
FittingC22×C4×C67C2
socle, cosocleC22×C67C23
prime radicalC2×C22⋊D67C2
hypercenterC22×C4D67
hypocenterC67C4×D4
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1072

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C22⋊D67)⋊C8, C8×C22⋊D67, #16863464, …
maximal normal subgroup of(C22⋊D67)⋊C8, C8×C22⋊D67, #16863464, …
maximal quotient ofC4×C22⋊Dic67, C4×(C2×D67)⋊C4, C4×Dic67⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2144, 107);