Finite Group Databasebeta

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C4×2−1+4×D73 #33992589

order18688
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×2−1+4×D73

Splittings

FittingC4×2−1+4×C73 ⋊ C2
SylowC73 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C24×D73
commutatorC2×C73C25×C4
FrattiniC22C25×D73
FittingC4×2−1+4×C73C2
socle, cosocleC22×C73C26
prime radicalC2×2−1+4×D73C2
hypercenterC4×2−1+4D73
hypocenterC73C2×C4×2−1+4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1076173);