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C2×Q8×GO+(4,𝔽2) #11902686

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×GO+(4,𝔽2)

Splittings

FittingC2×C32×Q8 ⋊ D4
SylowC32 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC22×C32C22×D4
prime radicalC22×GO+(4,𝔽2)C22
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32C2×D4×Q8
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×Q8

2418 conjugacy classes of subgroups; only the 503 normal subgroups are shown.

normal subgroups only

This group has 2418 conjugacy classes of subgroups — too many to draw. Only its 503 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 136697);