Finite Group Databasebeta

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#1043×#1313 #72242170

order12800
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#1043×#1313

Splittings

FittingC52×#1313 ⋊ C4
SylowC52 ⋊ C4×#1313

Subgroups

subgroupG/H
centerC2×C4C42×#1043
commutatorC4×C52C42×C8
FrattiniC4×C8C22×#1043
FittingC52×#1313C4
socleC22×C52C4×#97
prime radicalC22×C5⋊D5C2×#97
cosocleC4×C8×C5⋊D5C23
hypercenter#1313#1043
hypocenterC52C4×#1313
LCSG ▷ C4×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ #1313

3216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3200

Conjugacy classes & character table

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

Relationships

maximal subgroup of#1043×#12067, #72269242
maximal normal subgroup of#1043×#12067, #72269242

GAP

Past the SmallGroups library coverage — no SmallGroups id.