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C2×C5×#4033 #13106650

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#4033

Splittings

SylowC52 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23×C5C22×D5
commutatorC2×C5C23×C4×C5
FrattiniC22C23×C5×D5
FittingC2×C52×C4⋊C4C2
socle, prime radicalC23×C52C23
cosocleC22×C5C24×C5
hypercenterC2×C5×C4⋊C4D5
hypocenterC5C2×C4×C5×Q8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C5 ◁ C2×C5×C4⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9002);