Finite Group Databasebeta

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C2×#11752105 #14513716

order1920
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11752105

Splittings

SylowC5 ⋊ C2×#5386

Subgroups

subgroupG/H
centerC23C2×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FrattiniC22C22×C5⋊S4
FittingC2×C4×C5×Q8D3
socleC23×C5C2×S4
prime radicalC22×C5×SL(2,𝔽3)C22
hypercenterC22×C4C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

534 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 97 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) = 640

Conjugacy classes & character table

158 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 239414);