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C2×#22626552 #34031164

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22626552
unambiguous semidirect productD73⋊#2897

Splittings

FittingC2×H(5,𝔽2)×C73 ⋊ C4
SylowC73 ⋊ C2×#2897

Subgroups

subgroupG/H
centerC22C22×C22⋊#64408
commutatorC4×C73C24×C4
FrattiniC4C24×#64408
FittingC2×H(5,𝔽2)×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC2×H(5,𝔽2)×D73C2
cosocleC4×D73C25
hypercenterC2×H(5,𝔽2)#64408
hypocenterC73C2×#2897
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

5226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1114748);