Finite Group Databasebeta

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D4×#87855 #72253144

order3200
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD4×#87855

Splittings

SylowC52 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC2×C4C22×#1043
commutatorC2×C52C23×C8
FrattiniC22C23×#1043
FittingC4×C52×D4C4
socleC22×C52C23×C4
prime radicalC2×D4×C5⋊D5C4
cosocleC2×#1039C24
hypercenterC4×D4#1043
hypocenterC52C2×C8×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C4×D4

2464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72253148, C8×D4×#1043, #72253177
maximal normal subgroup of#72253148, C8×D4×#1043, #72253177
maximal quotient of#72253148

GAP

Past the SmallGroups library coverage — no SmallGroups id.