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C2×#22625778 #34020882

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22625778
unambiguous semidirect productD73⋊#1793

Splittings

FittingC2×2−1+4×C73 ⋊ C4
SylowC73 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC22#17989528
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×2−1+4×C73C4
socleC22×C73#379
prime radicalC2×2−1+4×D73C2
cosocleC2×C4×D73C24
hypercenterC2×2−1+4#64408
hypocenterC73C2×#1793
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

3682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1104466);