Finite Group Databasebeta

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C2×C4×#14556582 #33244473

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C4×#14556582

Splittings

SylowC73 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC23×C4C22×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×C4×C4⋊C4×C73C2
socle, prime radicalC24×C73C24
cosocleC23×C73C25
hypercenterC2×C4×C4⋊C4D73
hypocenterC73C2×C4×#125
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18688

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 328057);