Finite Group Databasebeta

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C2×Dic7×2−1+4 #14260406

order1792
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×Dic7×2−1+4

Splittings

SylowC7 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D7
commutatorC2×C7C25×C4
FrattiniC22C25×D7
Fitting, prime radicalC22×C7×2−1+4C2
socleC23×C7C25
cosocleC22×C7C26
hypercenterC22×2−1+4D7
hypocenterC7C2×C4×2−1+4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076178);