Finite Group Databasebeta

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C2×#97×#1043 #72242353

order6400
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×#97×#1043

Splittings

FittingC2×C52×#97 ⋊ C4
SylowC52 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC22×C4C22×#1043
commutatorC2×C52C2×C43
FrattiniC2×C4C23×#1043
FittingC2×C52×#97C4
socleC23×C52C2×C42
prime radicalC23×C5⋊D5C22×C4
cosocleC2×C4×C5⋊D5C24
hypercenterC2×#97#1043
hypocenterC52C2×C4×#97
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C2×#97

7160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#442×#1043, C2×#347×#1043, C2×#444×#1043
maximal normal subgroup ofC2×#442×#1043, C2×#347×#1043, C2×#444×#1043
maximal quotient ofC2×#347×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.