Finite Group Databasebeta

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C2×#19132514 #25005584

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#19132514

Splittings

SylowC43 ⋊ C2×#1312

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C2×C4×C16
FrattiniC4×C8C22×D43
FittingC2×C4×C16×C43C2
socle, prime radicalC23×C43C4×C8
cosocleC4×C8×C43C23
hypercenterC2×C4×C16D43
hypocenterC43C2×#1312
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 78555);