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2−1+4×D373 #37560254

order23872
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×D373

Splittings

Fitting2−1+4×C373 ⋊ C2
SylowC373 ⋊ C2×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×D373
commutator, socle, cosocleC2×C373C25
Fitting2−1+4×C373C2
hypercenter2−1+4D373
hypocenterC373C2×2−1+4
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C2 ◁ 2−1+4

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5968

Conjugacy classes & character table

3196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 1381);