Finite Group Databasebeta

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C4×C22⋊D463 #28414619

order14816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D463

Splittings

FittingC22×C4×C463 ⋊ C2
SylowC463 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D463
commutatorC2×C463C22×C4
FrattiniC22C22×D463
FittingC22×C4×C463C2
socle, cosocleC22×C463C23
prime radicalC2×C22⋊D463C2
hypercenterC22×C4D463
hypocenterC463C4×D4
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7408

Conjugacy classes & character table

3716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D463)⋊C8, C8×C22⋊D463, #44444861, …
maximal normal subgroup of(C22⋊D463)⋊C8, C8×C22⋊D463, #44444861, …
maximal quotient ofC4×C22⋊Dic463, C4×(C2×D463)⋊C4, C4×Dic463⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14816, 107);